At the start of France's bitterly contested presidential election campaign, critics predicted that Jean-Luc Mélenchon's confrontational approach to politics – including calls for "civic insurrection" and talk of a 100% tax band for those earning more than €1m – would see him shot down in flames well before the first round in three weeks.

Instead, the French seem to be taking to him. Opinion polls put Mélenchon on as much as 14% and rising, placing him above perennial middle man François Bayrou and at the heels of Marine Le Pen, leader of the far right Front National, who is in third place.

Mélenchon, 60, who graduated in philosophy, represents the Front de Gauche, or Left party, having abandoned the Socialist party in 2008. He is standing on an eclectic manifesto entitled "Humans First". Some on the left have expressed fears that the popularity of Mélenchon's radical programme could threaten the Socialist candidate, François Hollande, who will need to harvest Left party votes in an eventual run-off against incumbent president Nicolas Sarkozy. The danger for Hollande is that drifting too far on to Mélenchon's terrain could alienate the centrist voters he also needs.

Mélenchon, an entertaining loose cannon, has described Hollande as being as useful as the "captain of a pedalo" in a storm. But his most virulent outbursts are aimed at Le Pen, whom he has called a "filthy beast spitting hatred", a "bat" and a "dark presence". His programme veers from workers' rights, controlling the banks, escaping from the European Union in its current form and forging a new alliance, to ecological planning and dismantling Nato. In a recent speech he moved from getting rid of the French diplomatic service and the "absurd free market" and "taking apart all organisations that represent north American hegemony" to arguing the merits of France's Ariane space project and boosting the UN. It is an ambitious programme, but one that the former teacher and government minister – who like all the lesser candidates benefits from rules giving everyone equal broadcast time – defends bullishly.

Polls suggest Hollande and Sarkozy will be neck and neck with around 28% in the first round of the election on 22 April, but give Hollande victory with 54% against Sarkozy's 46% in a run-off a fortnight later.

A spokesman for Hollande said he did not believe Mélenchon would get more than 10% of votes in the first round. He rejected polls that suggest Le Pen could repeat the triumph in 2002 of her father, Jean-Marie Le Pen, and win her way into the second round, knocking out Sarkozy. "I thought it might be possible at one point, but not now," the Hollande spokesman said.

The five other candidates are expected to poll in single figures. IFOP's rolling opinion poll puts Europe Ecology candidate Eva Joly on 2.5%, Philippe Poutou of the New Anticapitalist party on 0.5%, Nathalie Arthaud from the Worker's Struggle party on 0.5%, Jacques Cheminade of the Solidarity and Progress party on 0%, and Nicolas Dupont-Aignan of Arise the Republic on 1%.

Mélenchon's supporters are simply hoping that their man stays on a roll. On his blog one post is entitled: "It's about to get bloody."